- #1
aerograce
- 63
- 1
When I am browsing through my rotational dynamics chapter, I raise myself a question on the direction of frictional force under all kinds of possible circumstances:
1. Pure rolling
For pure rolling, the frictional force will always be 0;
2. Non-pure rolling
For this situation, I will analyse with a model: A rolling ball lying on a level ground. And to simplify my listing, I will ignore some situations if they are similar to each other.
2.1 ω anti-clockwise v left
(1) ωR<v
Frictional force will tend to slow V down and increase ω, hence it is to the right;
(2) ωR>v
Frictional force will tend to increase V up and slow ω down. Hence it is to the left;
2.2 ω anti-clockwise v right
At first, the frictional force will be to the left(Slow down both ω and v)
But later, I think two situations may occur:
ω is not sufficiently large but v is sufficiently large, ω will be decreased to 0. And continuously, frictional force will be to the left to increase ω clockwisely until pure rolling occurs.
v is not sufficiently large but ω is sufficiently large, v will be decreased to 0. And after that, frictional force will be to the left to increase v leftwards until pure rolling occurs.
If ω and v just happen to be such nice that it will be decreased to 0 at the same time, the object will just stop then.
My idea in analyzing the frictional force is that: Non-pure rolling will always tend to transit itself into pure-rolling condition.
Thank you for spending time on reading this but could you please tell me whether my analysis is correct?
1. Pure rolling
For pure rolling, the frictional force will always be 0;
2. Non-pure rolling
For this situation, I will analyse with a model: A rolling ball lying on a level ground. And to simplify my listing, I will ignore some situations if they are similar to each other.
2.1 ω anti-clockwise v left
(1) ωR<v
Frictional force will tend to slow V down and increase ω, hence it is to the right;
(2) ωR>v
Frictional force will tend to increase V up and slow ω down. Hence it is to the left;
2.2 ω anti-clockwise v right
At first, the frictional force will be to the left(Slow down both ω and v)
But later, I think two situations may occur:
ω is not sufficiently large but v is sufficiently large, ω will be decreased to 0. And continuously, frictional force will be to the left to increase ω clockwisely until pure rolling occurs.
v is not sufficiently large but ω is sufficiently large, v will be decreased to 0. And after that, frictional force will be to the left to increase v leftwards until pure rolling occurs.
If ω and v just happen to be such nice that it will be decreased to 0 at the same time, the object will just stop then.
My idea in analyzing the frictional force is that: Non-pure rolling will always tend to transit itself into pure-rolling condition.
Thank you for spending time on reading this but could you please tell me whether my analysis is correct?